
10 E. Beltrami
this typical equation can be written in the two equivalent forms
(3)
Eshspbsq - 7pq, ~rkrqarp - 7pq.
Indicating with A, B, H, K, I" the determinants formed respectively with the elements
a,
b, c, h, k, 7, one has, from these last equations, I' = HB = KA. But, by the definition of
the quantities h, k, one has as well H = CA, K = CB; hence
F = ABC,
that is, the determinant of the transformed function is equal to that of the original one
multiplied by the products of the moduli of the two substitutions.
Let us suppose initially that the linear ...